Question
The supermarket is having a sale if you purchase 3 of an item Maggie bought macaroni and cheese and ramen with this sale in total she spent $9
Each box of Mac and cheese cost $1.25 identify the equation that will determine the amount for each package of ramen
Each box of Mac and cheese cost $1.25 identify the equation that will determine the amount for each package of ramen
Answers
GPT-4o mini
To determine the cost of each package of ramen, let's denote the following:
- Let \( x \) be the cost of one package of ramen.
- The price of one box of macaroni and cheese is given as $1.25.
Maggie bought a total of 3 items, and we need to let \( m \) be the number of macaroni and cheese boxes she bought and \( r \) be the number of ramen packages. Since the total she spent is $9, and we know each box of macaroni and cheese costs $1.25, we can set up the following equation based on her purchases:
Assuming she bought \( m \) boxes of macaroni and cheese and \( r \) packages of ramen, we write the total cost equation as:
\[
1.25m + xr = 9
\]
Given that she bought a total of 3 items (mac and cheese and ramen), we can also express this as:
\[
m + r = 3
\]
Now, if we know how many boxes of macaroni and cheese she bought, we can solve for \( r \) using the second equation.
For instance, if she bought \( m = 2 \) box of macaroni and cheese, then \( r \) would be:
\[
r = 3 - m = 3 - 2 = 1
\]
Substituting into the total cost equation gives:
\[
1.25(2) + x(1) = 9
\]
This simplifies to:
\[
2.5 + x = 9
\]
By isolating \( x \), we find:
\[
x = 9 - 2.5 = 6.5
\]
Thus, in general terms, the equation that relates the cost of each package of ramen to the number of macaroni and cheese boxes purchased can be described by combining the equations. Simply substitute \( r = 3 - m \) into the total cost equation:
\[
1.25m + x(3 - m) = 9
\]
This equation can now be used to determine the cost \( x \) of each package of ramen for any given number of macaroni and cheese boxes \( m \) that she might purchase.
- Let \( x \) be the cost of one package of ramen.
- The price of one box of macaroni and cheese is given as $1.25.
Maggie bought a total of 3 items, and we need to let \( m \) be the number of macaroni and cheese boxes she bought and \( r \) be the number of ramen packages. Since the total she spent is $9, and we know each box of macaroni and cheese costs $1.25, we can set up the following equation based on her purchases:
Assuming she bought \( m \) boxes of macaroni and cheese and \( r \) packages of ramen, we write the total cost equation as:
\[
1.25m + xr = 9
\]
Given that she bought a total of 3 items (mac and cheese and ramen), we can also express this as:
\[
m + r = 3
\]
Now, if we know how many boxes of macaroni and cheese she bought, we can solve for \( r \) using the second equation.
For instance, if she bought \( m = 2 \) box of macaroni and cheese, then \( r \) would be:
\[
r = 3 - m = 3 - 2 = 1
\]
Substituting into the total cost equation gives:
\[
1.25(2) + x(1) = 9
\]
This simplifies to:
\[
2.5 + x = 9
\]
By isolating \( x \), we find:
\[
x = 9 - 2.5 = 6.5
\]
Thus, in general terms, the equation that relates the cost of each package of ramen to the number of macaroni and cheese boxes purchased can be described by combining the equations. Simply substitute \( r = 3 - m \) into the total cost equation:
\[
1.25m + x(3 - m) = 9
\]
This equation can now be used to determine the cost \( x \) of each package of ramen for any given number of macaroni and cheese boxes \( m \) that she might purchase.